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P H I L I P C H A N
R Y A N S T A N S I F E R
M A R 2 4 , 2 0 1 7
A Closer Look at Computing: The Million-Dollar Algorithms
P H I L I P C H A N
Ranking Web Pages
Basic Problem
Input: Search query (keywords)
Web pages
Output Ranking of web pages relevant to the search query
Basic Problem
Input: Search query (keywords)
Web pages
Output Ranking of web pages relevant to the search query
If given 10 web pages and a search query (e.g. internet)
How would your rank the web pages?
Search Engines in the 1990s
Altavista
Excite
Infoseek
Webcrawler
…
Internet Archive: archive.org/web
Search Engines in the Early 2000s
Many search engines faded away
Google began to dominate
Secret Sauce of Google
Google did not advertise itself
Mostly by word of mouth
“free advertisement” from the press
Why did Google start to dominate?
What is the secret sauce of Google?
Brief History of Google
1996 -- 2 graduate students at Stanford U.
1997 – google.com was registered
1998 – [to be filled in later]
1998 – $100K investment, company incorporated
2004 – initial public offering (NASDAQ)
Secret Sauce of Google
A different way to rank web pages
In addition to words on a page
They use links between pages
How would you use links to rank pages?
Brief History of Google
1996 -- 2 graduate students at Stanford U.
1997 – google.com was registered
1998 -- publication of their algorithm in WWW Conf.
1998 – $100K investment, company incorporated
2004 – initial public offering (NASDAQ)
Algorithm: Page Rank
Input
Links between web pages
Output
Score for each web page
https://www.youtube.com/watch?v=Q9HjeFD62Uk
8:27-13:43
P H I L I P C H A N
Mystery Million-Dollar Problem
What is common among these tasks?
With a grocery shopping list
you try to gather all the items and leave quickly
Given a truck load of packages
a UPS/FedEx driver tries to deliver them quickly
Given locations of holes on a circuit board
Drill all the holes quickly
Common Problem
Given an initial location and other locations
Find the shortest route:
Start from an initial location
Visit each of the other locations exactly once
Go back to the initial location
Traveling Salesman Problem (TSP)
Traveling Salesman Problem (TSP)
https://www.youtube.com/watch?v=Q9HjeFD62Uk
36:12- 38:50
A Closer Look at TSP
Consider the initial location is Home
A, B, C are other locations
1st visit 2nd visit 3rd visit
Home A
B
C
A Closer Look at TSP
Consider the initial location is Home
A, B, C are other locations
1st visit 2nd visit 3rd visit
Home A B
C
B A
C
C A
B
A Closer Look at TSP
Consider the initial location is Home
A, B, C are other locations
1st visit 2nd visit 3rd visit
Home A B C
C B
B A C
C A
C A B
B A
A Closer Look at TSP
Consider the initial location is Home
A, B, C are other locations
1st visit 2nd visit 3rd visit Last visit
Home A B C Home
C B
B A C
C A
C A B
B A
A Closer Look at TSP
Consider the initial location is Home
A, B, C are other locations
3 * 2 * 1 = 6 possible routes
1st visit 2nd visit 3rd visit Last visit
Home A B C Home
C B
B A C
C A
C A B
B A
4 locations
1st visit
4 choices
2nd visit
3 choices
3rd visit
2 choices
4th visit
1 choice
4*3*2*1 = 24 possible routes
n locations
1st visit
n choices
2nd visit
n-1 choices
…
nth visit
1 choice
# of possible routes?
n locations
1st visit
n choices
2nd visit
n-1 choices
…
nth visit
1 choice
# of possible routes?
n*(n-1)*(n-2) …. *2*1 = n!
Computer checks 1 billion routes per second
# of locations # of possible routes Completion time
10 3.6M 0.003 s
Computer checks 1 billion routes per second
# of locations # of possible routes Completion time
10 3.6M 0.003 s
15 ?
Computer checks 1 billion routes per second
# of locations # of possible routes Completion time
10 3.6M 0.003 s
15 1.3 x 10^12 22 minutes
20 ?
Computer checks 1 billion routes per second
# of locations # of possible routes Completion time
10 3.6M 0.003 s
15 1.3 x 10^12 22 minutes
20 2.4 x 10^18 77 years
100 ?
Computer checks 1 billion routes per second
# of locations # of possible routes Completion time
10 3.6M 0.003 s
15 1.3 x 10^12 22 minutes
20 2.4 x 10^18 77 years
100 9.3 x 10^157 3 x 10^141 years
TSP and Bees
https://www.youtube.com/watch?v=Q9HjeFD62Uk
38:50-42:30
$1M prize
Clay Mathematical Institute
claymath.org
Millennium Prize Problems (7)
$1M each
P=NP?
Does an efficient algorithm for TSP exist?
A yes or no answer will win the prize
If yes, (a large number of) problems in the same class can be solved efficiently.
Part 2
Thank You
cs.fit.edu/~pkc/cs4hs Summer Camps
July
8pm, astronomy lecture, Olin Engineering, Rm 118 Across the courtyard
Between this building and the parking lot
9pm, 32-inch telescope
Questions?
